On bounds in Borsuk's problem

In this work we discuss various estimates connected with Borsuk’s conjecture. We consider some series of distance graphs and corresponding induced dual configurations embedded to the spaces of "small dimensions" as well as in case of growing dimension. We then apply a modification of the linear algebra method to the graphs. This leads us to lower estimates of f(d) - the minimal possible number of subsets of "smaller diameter" in terms of Borsuk’s problem in Rd.